In an internal combustion engine of the carburetor type, misfire easily takes place when the engine operates under a slow deceleration rate while the throttle valve is fully closed, for example, when a vehicle is operating on a long downhill slope, because the amount of air introduced into the intake system is reduced due to the fully closed throttle valve while an excess amount of fuel is sucked into the intake system due to the high vacuum level in the intake system, so that an unburnt air-fuel mixture is exhausted into the exhaust system. This not only causes an inefficiency to occur in the fuel consumption of the engine, but also a so-called "afterburning" when the engine is provided with a catalytic converter in the exhaust system, because the unburnt air-fuel mixture is explosively burnt in the exhaust system due to the high temperature of the catalytic converter. When afterburning is taking place, the catalytic material packed in the catalytic converter becomes overheated and inactivated.
To overcome this difficulty, an apparatus has already been proposed for stopping the supply of fuel to the internal combustion engine during the operation of the engine deceleration. In this known apparatus, the deceleration operation is detected by the fully closed position of the throttle valve and by an engine rotational speed higher than the predetermined speed. In this case, the predetermined rotational speed should be determined so that it is a high enough rotational speed, for example 2500 r.p.m, with respect to the idle rotational speed, for example 750 r.p.m. This is because, if the predetermined rotational speed is near the idler rotational speed, the engine can easily be stopped when the engine rotational speed is being quickly decelerated due to the delay in the starting of the resupplying operation of fuel to the engine. Such quick deceleration of the engine rotational speed is realized, for example, when the clutch is disengaged; or when the engine rotational speed is abruptly increased under no load while the vehicle is being stopped.
However, the rotational speed at which the supply of fuel is stopped is high, the fuel stopping operation is not carried out when the vehicle is running in the city in which the rotational speed of the engine is normally low. Thus, the fuel consumption efficiency is reduced.